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math.CT2026
Directed univalence for simplicial objects in an -topos
Evan Cavallo, Emily Riehl, Christian Sattler
A fundamental component of homotopy type theory, a synthetic theory of -groupoids, is Voevodsky's univalence axiom. Univalence characterizes the identity types in the unive…
math.CT2025
The algebraic small object argument as a saturation
Evan Cavallo, Christian Sattler
We analyze the structure of left maps in algebraic weak factorization systems constructed using Garner's algebraic small object argument. We find that any left map can be construct…